The Competition Commission ruled in March that the operator must sell Gatwick, Stansted and either Edinburgh or Glasgow airports.
But an appeal tribunal reversed the decision.
BAA has already sold Gatwick but the judgement will not affect that deal.
Meanwhile the appeal rejected BAA claims that ordering them to sell airports within two years was too quick.
BAA had argued that there was a conflict of interest because of links between a member of commission panel member Professor Peter Moizer and an organisation interested in buying the airports.
The company claimed the professor should not have been on the panel as he was a fee-paid adviser to the Greater Manchester Pension Fund, which had links with Manchester Airport Group.
A BAA spokesman said: "We are pleased that the Competition Appeal Tribunal upheld our appeal on the grounds of apparent bias.
Further discussions should now take place with the Competition Commission, as the CAT suggests, to determine the appropriate response to this judgement."